https://en.formulasearchengine.com/api.php?action=feedcontributions&feedformat=atom&user=149.156.17.142formulasearchengine - User contributions [en]2026-05-23T16:58:53ZUser contributionsMediaWiki 1.43.0-wmf.28https://en.formulasearchengine.com/index.php?title=Blasius_function&diff=26969Blasius function2013-08-09T14:13:43Z<p>149.156.17.142: link to the article about Blasius functions in Polish language Wikipedia</p>
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<div>In mathematics, the '''Hahn–Exton q-Bessel function''' or the '''third [[Jackson q-Bessel function]]''' is a [[q-analog|''q''-analog]] of the [[Bessel function]], introduced by {{harvs|txt|last=Hahn|authorlink=Wolfgang Hahn|year=1953}} in a special case and by {{harvs|txt|last=Exton|authorlink=Harold Exton|year=1983}} in general.<br />
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The Hahn–Exton ''q''-Bessel function is given by <br />
:<math> J_\nu^{(3)}(x;q) = \frac{x^\nu(q^{\nu+1};q)_\infty}{(q;q)_\infty} \sum_{k\ge 0}\frac{(-1)^kq^{k(k+1)/2}x^{2k}}{(q^{\nu+1};q)_k(q;q)_k} </math><br />
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==References==<br />
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*{{Citation | last1=Exton | first1=Harold | title=q-hypergeometric functions and applications | url=http://books.google.com/books?id=3kHvAAAAMAAJ | publisher=Ellis Horwood Ltd. | location=Chichester | series=Ellis Horwood Series: Mathematics and its Applications | isbn=978-0-85312-491-7 | mr=MR708496 | year=1983}}<br />
*{{Citation | last1=Hahn | first1=Wolfgang | authorlink=Wolfgang Hahn | title=Die mechanische Deutung einer geometrischen Differenzengleichung | language=German | doi=10.1002/zamm.19530330811 | zbl=0051.15502 | year=1953 | journal=Zeitschrift für Angewandte Mathematik und Mechanik | issn=0044-2267 | volume=33 | pages=270–272}}<br />
*{{citation|first=M. E. H.|last= Ismail|title= Some Properties of Jacksons Third q-Bessel Function|series=preprint|year=2003}}<br />
*{{Citation | last1=Swarttouw | first1=René F. | title=An addition theorem and some product formulas for the Hahn-Exton q-Bessel functions | doi=10.4153/CJM-1992-052-6 | mr=1178574 | year=1992 | journal=[[Canadian Journal of Mathematics]] | issn=0008-414X | volume=44 | issue=4 | pages=867–879}}<br />
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{{DEFAULTSORT:Hahn-Exton q-Bessel function}}<br />
[[Category:Special functions]]<br />
[[Category:Q-analogs]]</div>149.156.17.142